Reduced order models (ROM) are commonly employed to solve parametric problems and to devise inexpensive response surfaces to evaluate quantities of interest in real-time. There are many families of ROMs in the literature and choosing among them is not always a trivial task. This work presents a comparison of the performance of a priori and a posteriori proper generalised decomposition (PGD) algorithms for an incompressible Stokes flow problem in a geometrically parametrised domain. This problem is particularly challenging as the geometric parameters affect both the solution manifold and the computational spatial domain. The difficulty is further increased because multiple geometric parameters are considered and extended ranges of values are analysed for the parameters and this leads to significant variations in the flow features. Using a set of numerical experiments involving geometrically parametrised microswimmers, the two PGD algorithms are extensively compared in terms of their accuracy and their computational cost, expressed as a function of the number of full-order solves required.
翻译:减序模型(ROM)通常用于解决参数问题和设计低廉的反应面,以评价实时的兴趣量。文献中有许多ROM系列,选择其中的ROM并不总是一件微不足道的任务。这项工作比较了在几何相近的域内无法压缩的Stokes流动问题的先验和后验的适当一般分解算法(PGD)的性能。由于几何参数既影响多种解决办法,又影响计算空间域,这一问题尤其具有挑战性。由于考虑到多个几何参数,对参数的扩大值范围进行了分析,从而导致流动特征的显著变化,因此难度进一步加大。使用一套涉及几何相近微缩微粒的数值实验,两种PGD算法在精确性和计算成本方面进行了广泛的比较,表现为所需全序解算数的函数函数。